Multipying & Dividing Rules

How does an expression like simplify? Notice that both terms have the same base. When a product of two or more terms has the same base to a power, the exponents can be added.

Product of Powers Rule:xⁿ·x^m = x^n+m

Why does this rule work? Using the expression above and writing out the expansion of each term creates the following steps:

This rule is a nice "shortcut" for the multiplication of terms, but it only applies to exponents with the same base. Therefore, it will not work for , because the bases are not the same.